Like in Love With You by Emma R. Alban

Mean Girls meets Northanger Abbey in this sharp and sexy Regency Romance that begs the question: what if Cady and Regina just… kissed?   When Catherine Pine relocates to Bath in 1817, she comes face-to-face with her mother’s arch nemesis and her daughter—the wildly popular Lady Rosalie. Twenty-five years after a horrible betrayal, Catherine’s mother sees the perfect opportunity for revenge: Catherine must win the favor of Lady Rosalie’s suitor and unofficial betrothed, the most eligible Mr. Dean.

Only Catherine soon discovers that Lady Rosalie is by far the wittiest, cleverest, most intriguing young woman Catherine’s ever met, and she’s instantly smitten. Which is a problem.
 
Meanwhile, Lady Rosalie feels trapped in her relationship with Mr. Dean and in her role as Bath’s resident mean girl. But when she notices newcomer Catherine gunning for her spot as queen bee, Rosalie finally feels a spark again–something she absolutely doesn’t want to extinguish.
 
As Rosalie and Catherine circle Mr. Dean, and their mothers force them into increasingly absurd contests of wit and feminine charms, the two women somehow find themselves falling for each other, scheme, by barb, by catty jab…Is it possible that their sizzling rivalry can become a match to last?